Variant Coverage and Imputation Differences Across Ancestries

Why Variant Coverage Matters

Trans-ancestry fine-mapping uses association evidence from more than one ancestry group to distinguish candidate causal variants. That comparison is only as informative as the variants that were actually measured or reliably imputed in each group. A variant may be directly genotyped in one group, well imputed in another, poorly imputed in a third, and absent from the analyzed data in a fourth. These cases do not provide equivalent evidence.

Coverage and measurement quality interact with allele frequency. A variant that is common in one sampled ancestry group may be rare in another, giving the latter group less information even when sample sizes are similar. Consequently, a weaker association statistic can reflect lower information rather than a smaller genetic effect. Conversely, a variant not available for analysis cannot be treated as a tested variant with a null result.

These terms refer to properties of the data and analysis, not to whether a variant is causal. The set of variants available to fine-map can differ across groups, and the evidence for a variant that is available can differ because of allele frequency, sample size, imputation quality, linkage disequilibrium (LD), phenotype measurement, or other design features. The focus here is how coverage and genotype information affect the candidate set and the interpretation of association evidence.

A Simple Information Model

To make the information differences explicit, consider an approximate additive association model for one ancestry group. Let \(G\) be a centered genotype count for the effect allele, with allele frequency \(f\), and let \(Y\) be a quantitative phenotype. Assume the phenotype follows a linear model with a constant per-allele effect \(\beta\), independent errors with variance \(\sigma^2\), and no unmodeled structure that confounds the association. Assume also that the analyzed individuals are independent and that the association test is calibrated for the model. For a well-measured biallelic genotype under Hardy–Weinberg equilibrium, the genotype variance is approximately \(2f(1-f)\).

In a simplified information calculation, let \(q\) denote the fraction of full-genotype association information retained by the analyzed genotype data. Here \(q=1\) represents perfect genotype information, while lower values represent information loss. This is an analytical approximation: an imputation INFO statistic from a particular pipeline is not automatically an exact value of \(q\) for every association model.

For a phenotype standardized to have residual standard deviation \(\sigma=1\), the approximate standard error of the per-allele effect is \(SE(\hat{\beta})\approx 1/\sqrt{I}\). More generally, \(SE(\hat{\beta})\approx \sigma/\sqrt{I}\). The standardized association statistic has an approximate normal distribution with variance one and mean, or noncentrality parameter, \(\delta\):

This relationship separates three quantities that are easy to conflate: the effect \(\beta\), the uncertainty in its estimate, and the sampling variation in the observed statistic \(Z\). For the same nonzero standardized effect, greater information increases the magnitude of the noncentrality parameter and reduces the standard error. It does not make every realized \(Z\) larger, nor does it imply that the expected absolute value of \(Z\) scales with \(\sqrt{I}\). Under the null, for instance, \(Z\) is approximately standard normal whatever the information level, so its expected absolute value is unchanged.

Coverage Changes the Candidate Set

Fine-mapping compares candidate variants using the evidence available for those variants. If a variant is not present in an ancestry-specific summary-statistic file, there is no association statistic for that variant in that data set. Its absence may reflect genotyping design, quality-control filters, imputation limitations, or data-processing choices. It is not equivalent to an observed estimate near zero with a large standard error, and it is not evidence that the variant has no effect.

Different candidate sets also affect posterior summaries. A posterior inclusion probability (PIP) is conditional on the model, prior, data, and variants included as candidates. If a candidate is excluded because it is unavailable, the candidate space changes and the posterior probabilities for the remaining variants can change as well. PIPs computed over different variant sets therefore need not be directly comparable: a PIP can change because the evidence changed, because the candidate universe changed, or both. A missing candidate should not be assigned a likelihood of zero or a posterior probability of zero merely because its data were unavailable.

A practical first step is to make a coverage map for the locus. For every candidate, record whether it was directly genotyped, imputed and retained, filtered out, or not represented in that group’s analysis. If imputed, record the relevant quality measure and allele frequency. This makes a distinction between “tested with weak evidence” and “not tested” visible before interpreting the fine-mapping results.

Allele Frequency and the Meaning of Weak Evidence

Allele frequency affects association information even when every genotype is measured perfectly. Under the simple model, \(2f(1-f)\) is largest near \(f=0.5\) and becomes small as \(f\) approaches zero or one. Rare variants therefore tend to provide less information in a fixed sample, because fewer individuals carry the less common allele. If a variant is monomorphic in a sample, there is no genotype variation from which to estimate its association effect in that sample.

Ancestry-specific frequency differences can consequently create very different standard errors for the same variant. A non-significant association in a group where the variant is rare may be compatible with an effect similar to that in another group; the data may simply be imprecise. A non-significant result is not proof of no effect. Conversely, a small p-value in a larger or more informative group does not alone establish that the effect is larger there. Compare effect estimates and their uncertainty, and check whether the phenotype scale, allele coding, model, and analysis are sufficiently comparable.

Comparing Association Evidence Across Groups

A useful comparison starts by separating the association estimate from its precision. Under the simple model, a group with lower \(I\) has a larger standard error, so its estimate can be less precise even if the underlying effect is the same. The observed \(Z\) statistic combines the estimate and its standard error; a p-value additionally summarizes the statistic relative to a null distribution. Neither a \(Z\) statistic nor a p-value is an effect-size measure by itself.

Before comparing a variant across ancestry-specific results, check the following:

• Availability: Was the variant tested in both groups, and were the same variant and genomic alleles represented?
• Frequency: What was the effect-allele frequency in each group? Is there enough variation to estimate an effect?
• Genotype quality: Was the variant directly genotyped or imputed, and what quality threshold and metric were used?
• Effect and uncertainty: Are estimates reported on the same phenotype and effect-allele scale, with standard errors available?
• Analysis comparability: Were the phenotype definition, covariate adjustment, and association model sufficiently similar?

Allele harmonization is essential when interpreting signed effects: the same allele must be coded as the effect allele across groups. Even after harmonization, comparisons can be misleading if one group has low information or if the phenotype scales differ. Differences in LD can also cause neighboring variants to show different association patterns even when a causal variant is shared; that is distinct from coverage and imputation, but it reinforces why one marginal association statistic should not be read as a direct causal verdict.

Short Justification: Why Information Scales the Noncentrality

The scaling in the simplified model follows from the variance of a regression estimate. For independent observations with centered genotype \(G\), the variance of the estimated per-allele effect is approximately \(\sigma^2/[n\operatorname{Var}(G)]\). If \(\operatorname{Var}(G)\approx2f(1-f)\), and usable genotype information is a fraction \(q\) of the full-genotype information, then

Dividing an effect estimate by its standard error gives the standardized statistic. Under a true effect \(\beta\), its mean is approximately

This derivation assumes the approximate model and information fraction just stated. Real analyses can depart from it because of covariates, relatedness, case-control sampling, genotype uncertainty, imputation calibration, or imperfect phenotype modeling. The formula is a way to understand the direction and approximate size of information differences, not a substitute for the study’s reported standard errors and quality diagnostics.

Common Mistakes and Practical Consequences

• Calling an unavailable variant a null result. No analyzed genotype data means no association test for that variant in that group. It is missing evidence, not evidence for a zero effect.
• Equating non-significance with no effect. A large standard error, low allele frequency, or poor imputation can make an association hard to detect. Report the estimate and uncertainty rather than relying only on a significance threshold.
• Using the wrong scaling language. Under the simplified model, \(\sqrt{I}\) scales the magnitude of the noncentrality parameter for a fixed effect. It does not generally scale the expected absolute observed \(Z\), which includes sampling noise.
• Comparing PIPs without checking candidate sets. A PIP is conditional on the candidates and model used. Record coverage before interpreting differences in posterior probabilities.
• Treating an imputation metric as a universal correction. Quality metrics and their interpretation depend on the imputation pipeline and association analysis. Use them as diagnostics and check the study’s definitions.